Chapter 7 L&C quiz

Indirect Proofs always involve

a contradiction

Proofs always end with

a line which states the conclusion of the argument to be proved

in Natural Deduction, a proof is

a series of steps that show the premises lead, by way of valid rules of inference, to the conclusion

The RAA principle is the strategy behind

an indirect proof

The basic purpose of our system of inference rules for Natural Deduction proofs is to show that

any valid argument is valid

In the course materials, Conditional Proof was compared to the idea of

borrowing money

Proofs always begin with

one or more premises or assumptions

Given the following premises: 1.∼T ⊃ E 2. ∼K ⊃ (∼T ∨ ∼T) 3. M ⊃ (∼K ∨ ∼L) Select the conclusion that follows in a single step from the given premises.

M ⊃ (K ⊃ ∼L) 3, Impl

Given the following premises: 1.(S • ∼J) ∨ (∼S • ∼∼J) 2. S ∨ ∼S 3. ∼J ⊃ P Select the conclusion that follows in a single step from the given premises.

S ≡ ∼J 1, Equiv

Given the following premises: 1. (J • ∼N) ∨ T 2. ∼(J • ∼N) 3. ∼T Select the conclusion that follows in a single step from the given premises.

T 1, 2, DS

Can there be more than one correct proof of a valid argument?

Yes

Given the following premises:1. 1. ∼D ∨ ∼T 2. D ∨ (∼T • ∼R) 3. D Select the conclusion that follows in a single step from the given premises.

(D ∨ ∼T) • (D ∨ ∼R) 2, Dist

Given the following premises: 1.Q ⊃ (H • L) 2. H ⊃ ∼Q 3. L ⊃ ∼Q Select the conclusion that follows in a single step from the given premises.

(L ⊃ ∼Q) • (H ⊃ ∼Q) 2, 3, Conj

Given the following premises: 1.(S ⊃ R) ⊃ (J ⊃ T) 2. (P ⊃ R) ⊃ (S ⊃ R) 3. R ⊃ J Select the conclusion that follows in a single step from the given premises.

(P ⊃ R) ⊃ (J ⊃ T) 1, 2, HS

Given the following premises: 1. ∼N • ∼F 2. K ⊃ (N • F) 3. U ∨ (K • ∼N) Select the conclusion that follows in a single step from the given premises.

(U ∨ K) • (U ∨ ∼N) 3, Dist

Given the following premises: 1.F ⊃ J 2. A ⊃ (F • J) 3. A • (Q ∨ N) Select the conclusion that follows in a single step from the given premises.

A • (N ∨ Q) 3, Com

Given the following premises: 1.K ∨ ∼H 2. (K ∨ ∼H) ⊃ (B ⊃ J) 3. J ⊃ D Select the conclusion that follows in a single step from the given premises.

B ⊃ J 1, 2, MP

Given the following premises:1. 1. K ∨ ∼H 2. (K ∨ ∼H) ⊃ (B ⊃ J) 3. J ⊃ D Select the conclusion that follows in a single step from the given premises.

B ⊃ J 1, 2, MP

Given the following premises: 1.(C • ∼F) ⊃ E 2. G ∨ (C • ∼F) 3. ∼(C • ∼F) Select the conclusion that follows in a single step from the given premises.

C ⊃ (∼F ⊃ E) 1, Exp

Given the following premises: 1.N ∨ C 2. (N ∨ C) ⊃ (F ⊃ C) 3. ∼C Select the conclusion that follows in a single step from the given premises.

F ⊃ C 1, 2, MP

Given the following premises: 1. A 2. G ⊃ (A ⊃ ∼L) 3. ∼A ∨ ∼G Select the conclusion that follows in a single step from the given premises.

G ⊃ (∼∼L ⊃ ∼A) 2, Trans

Given the following premises: 1.(K • ∼T) ∨ (K • ∼H) 2. ∼M ⊃ (K • ∼H) 3. ∼(K • ∼H) Select the conclusion that follows in a single step from the given premises.

K • (∼T ∨ ∼H) 1, Dist

Given the following premises: 1. ∼∼N 2. K ⊃ ∼N 3. ∼N ∨ (K • S) Select the conclusion that follows in a single step from the given premises.

K • S 1, 3, DS

Given the following premises: 1.∼∼N 2. K ⊃ ∼N 3. ∼N ∨ (K • S) Select the conclusion that follows in a single step from the given premises.

K • S 1, 3, DS

Given the following premises: 1. G • ∼A 2. K ⊃ (G • ∼A) 3. G ⊃ M Select the conclusion that follows in a single step from the given premises.

K ⊃ ( ∼A • G) 2, Com

Given the following premises. 1.∼M ⊃ S 2. ∼M 3. (M ∨ H) ∨ ∼S Select the conclusion that follows in a single step from the given premises.

M ∨ (H ∨ ∼S) 3, Assoc

Given the following premises: 1.N ≡ R 2. (N • ∼R) ⊃ C 3. N Select the conclusion that follows in a single step from the given premises.

N ⊃ (∼R ⊃ C) 2, Exp

Given the following premises: 1. P • (∼H ∨ D) 2. ∼(∼P • ∼H) 3. (P ⊃ ∼H) • (∼P ⊃ H) Select the conclusion that follows in a single step from the given premises.

P • (H ⊃ D) 1, Impl

Given the following premises: 1. Q ⊃ (A ∨ ∼T) 2. T 3. A ∨ ∼T Select the conclusion that follows in a single step from the given premises.

Q ⊃ (∼∼A ∨ ∼T) 1, DN

Given the following premises: 1.A 2. (A ⊃ ∼T) ⊃ ∼G 3. Q ⊃ (A ⊃ ∼T) Select the conclusion that follows in a single step from the given premises.

Q ⊃ ∼G 2, 3, HS

Given the following premises: 1. ∼R ≡ ∼R 2. N • ∼T 3. R ⊃ ∼(N • ∼T) Select the conclusion that follows in a single step from the given premises.

R ⊃ (∼N ∨ ∼∼T) 3, DM

Given the following premises: 1.R • ∼S 2. R ⊃ ∼(S • ∼F) 3. ∼S ⊃ (F • N) Select the conclusion that follows in a single step from the given premises.

R ⊃ (∼S ∨ ∼∼F) 2, DM

Given the following premises: 1.∼U ⊃ (S • K) 2. R ⊃ (∼U • ∼U) 3. S ≡ ∼U Select the conclusion that follows in a single step from the given premises.

R ⊃ ∼U 2, Taut

'RAA' is an abbreviation for

Reductio ad Absurdum

In the course materials, Indirect Proof was compared to the idea of

troubleshooting a problem with your car battery

The guiding principle of reductio ad absurdum is that

whatever implies a contradiction is false.

Given the following premises: 1.∼I ∨ ∼∼B 2. M ⊃ ∼I 3. I Select the conclusion that follows in a single step from the given premises.

∼(I • ∼B) 1, DM

Given the following premises: 1.N 2. R ⊃ ∼N 3. ∼C • (T ⊃ R) Select the conclusion that follows in a single step from the given premises.

∼C 3, Simp

Given the following premises: 1. D ⊃ H 2. ∼D 3. ~(D • S) Select the conclusion that follows in a single step from the given premises.

∼D ∨ (D ⊃ H) 2, Add

Given the following premises: 1. D ⊃ H 2. ∼D 3. ∼(D ∨ S) Select the conclusion that follows in a single step from the given premises.

∼D ∨ (D ⊃ H) 2, Add

Given the following premises: 1. (S ⊃ ∼F) • (∼F ⊃ B) 2. S ∨ ∼F 3. ∼F Select the conclusion that follows in a single step from the given premises.

∼F ∨ B 1, 2, CD

Given the following premises: 1.∼E ⊃ P 2. ∼P 3. ∼(P ∨ ∼H) Select the conclusion that follows in a single step from the given premises.

∼P • ∼(P ∨ ∼H) 2, 3, Conj

Given the following premises: 1.Q ⊃ (H • ∼F) 2. ∼(Q • ∼M) 3. ∼G ⊃ (Q • ∼M) Select the conclusion that follows in a single step from the given premises.

∼Q ∨ ∼∼M 2, DM

Given the following premises: 1. ∼(Q • ∼S) 2. ∼F ⊃ (Q • ∼S) 3. H ∨ (Q • ∼S) Select the conclusion that follows in a single step from the given premises.

∼∼F 1, 2, MT